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We develop a diagrammatic scattering theory for interacting bosons in athree-dimensional, weakly disordered potential. We show how collisional energytransfer between the bosons induces the thermalization of the inelasticsingle-particle current which, after only few collision events, dominates overthe elastic contribution described by the Gross-Pitaevskii ansatz.

Inelastic Multiple Scattering of Interacting Bosons in Weak Random Potentials